What are the consequences of the issues you've found, in practical terms? Presumably they 1) make it more time-consuming (and thus more expensive) to fix bugs in those areas of the application, and 2) they make it more time-consuming to add new functionality to the application. (there may be more points, of course, depending on the issues you've found, and the codebase and application in general)
How much more time-consuming? If you can't quantify it, how do you expect them to buy your argument?
Duplicated code might, in grossly simplified terms mean that every bugfix takes twice as long (because they have to be fixed in two places, and in each, you need to test to make sure your fix didn't break anything). Code which isn't sufficiently general may have to be rewritten when new features are added, and that introduces a risk of breaking everything around it. How much will that cost?
My best suggestion is going to be to try to put numbers on how much these issues are going to cost down the line. Of course you can't make an accurate estimate, but you're definitely better qualified to come up with a rough guess than your audience is. So that's what you have to do.
Otherwise, you're just asking them to follow your hunch, your irrational instinct. While we'd say your instinct is probably right, it's going to be a hard sell to a non-technical audience. They're likely to say that "if even the programmer can't say how much it'll cost us in the long run if we don't fix these issues, how do we know they're issues at all?"
You might be able to do this by setting up simple scenarios ("Let's say we ignore these issues for now, and at some point after release, a critical bug in component X is found. Because of the messy code we never got around to fixing when we had the chance, this component is now intertwined with components Y and Z, so a fix will have to be tested against this much larger chunk of code to ensure it didn't break existing functionality. This'll take so many days every time a bug in this component is discovered, which could have been reduced to that many days if we fix this issue up front".), or by pulling in generally available statistics (how long does it take to fix bugs in clean vs. messy codebases? Did it pay off for other teams to clean up code smell early?